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Apr
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comment |
Hejhal's algorithm and computational methods for non-classical Maass wave forms
I think the paper on his home page is the same as the one he posted to the ArXiv: sites.google.com/site/mboris |
Apr
18 |
answered | Hejhal's algorithm and computational methods for non-classical Maass wave forms |
Apr
17 |
revised |
central/critical/special values of L-functions terminology
added 159 characters in body; edited body |
Apr
17 |
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central/critical/special values of L-functions terminology
I wrote the question in the "arithmetic" normalization, with $s$ going to $w+1-s$ in the functional equation. I know that "most" L-functions are not motivic, but my understanding is that the concept of special/critical values only makes sense for motivic L-functions. You wouldn't say, for example, that every integer is a critical point for the L-function of a Maass form. There are times when you want to normalize the L-function so that $s$ goes to $1-s$, but this is not one of those times. |
Apr
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asked | central/critical/special values of L-functions terminology |
Mar
21 |
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Is there an explicit expression for the imaginary part of some non-trivial zero of zeta,
Greg, Not even close: we can't even prove that for degree 2. It is not even known that the members of the Selberg class, of degree 2 or more, have Euler products whose local factors are the reciprocal of a polynomial. (I saw something along those lines -- I forget the details -- from Kaczorowski and Perelli, but what I wrote is definitely true for "degree more than 2.") |
Mar
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revised |
Is there an explicit expression for the imaginary part of some non-trivial zero of zeta,
added 1035 characters in body |
Mar
18 |
comment |
Is there an explicit expression for the imaginary part of some non-trivial zero of zeta,
Paul, It is conjectured that the factorization of L-functions into primitive L-functions is unique. This follows from the Selberg Orthonormality Conjecture. Unique factorization implies that you can't "split up" the cancellation of zeros of one L-function by part of the zeros of several different L-functions. So (assuming appropriate conjectures) the Artin L-function can only be entire if there is a cancellation of actual L-functions in the numerator and denominator. |
Mar
18 |
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Is there an explicit expression for the imaginary part of some non-trivial zero of zeta,
If an Artin L-function was genuinely a ratio, and not a product, of other L-functions (in other words, if it had infinitely many poles) then it does not deserve to be called an L-function! For this discussion I think it makes sense to assume all reasonable conjectures. |
Mar
18 |
answered | Is there an explicit expression for the imaginary part of some non-trivial zero of zeta, |
Feb
28 |
comment |
Small index subgroups of SL(3,Z)
Great answer. I wish I could "accept" two answers. |
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